Using chaos and symmetry to bootstrap quantum gravitational wormholes

An international research collaboration between Gabriele Di Ubaldo (RIKEN-Berkeley Center at UC Berkeley and RIKEN iTHEMS), Jan Boruch (University of California, Berkeley, US), Felix M. Haehl (University of Southampton, UK), Eric Perlmutter (Université Paris-Saclay and Institut des Hautes Études Scientifiques, France), and Moshe Rozali (University of British Columbia, Canada) published the new study in Physical Review Letters.

Random matrix theory provides a universal description of chaos in quantum systems, capturing statistical patterns among energy levels without requiring knowledge of microscopic details. The new challenge addressed is its extension to 2D Conformal Field Theories and their holographically dual 3D quantum gravity via the AdS₃/CFT₂ correspondence. In the AdS₃/CFT₂ correspondence, quantum gravity in a three-dimensional negatively curved spacetime is encoded in a two-dimensional conformal field theory on its boundary. The key difference is modular invariance, a symmetry stating that a theory on a 2D torus is invariant under modular transformations, which imposes stringent constraints and a rigid mathematical structure, seemingly incompatible with quantum chaos and random matrix theory.

Building on the 2023 work of Di Ubaldo and Perlmutter, “AdS₃/RMT₂ duality”, the researchers developed a general, nonperturbative framework called RMT₂ that uplifts the correlations of any random matrix model into fully modular-invariant quantities.

The team then used RMT₂ to predict quantum amplitudes for 3D wormholes with multiple torus-shaped boundaries. A wormhole is a tunnel-like geometric connection between otherwise separate regions or boundaries of spacetime. While it is not a shortcut for interstellar travel as in sci-fi movies, it encodes deeply quantum information about gravity and black holes. For the three-boundary wormhole, the team also performed a gravity calculation that agrees with the RMT₂ prediction.

By turning the earlier AdS₃/RMT₂ proposal into a general framework, the study advances a research direction that Gabriele helped pioneer and provides a new tool for probing black-hole microstates and, in the near future, solving AdS₃ quantum gravity.

For further details, please see the article in Physical Review Letters.